By Webster A. G.
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Extra info for Acoustical Impedance and the Theory of Horns and of the Phonograph (1919)(en)(8s)
The effect of the anharmonicity is taken into account by using in place of Eq. 12 the energy-level formula 61 -[(J +1) -- Xe(i +' ]hvi where xe is the anharmonicity factor, which is zero for simple harmonic motion. Derive the vibrational partition function for this energylevel formula. Since xe is small, any exponential function that has xe in the argument can be approximated by a two-term Taylor series expansion. Sketch the energy-level formula. Show that the partition-function sum must be cut off at j<-.
The electrons are considered to move freely within the confines of the volume V, uninhibited by the periodic point charges of the ion cores. The electrons thereby constitute an ideal gas of particles obeying Fermi-Dirac statistics. Because two spin states are associated with each translational energy state, the total number of quantum states accessible to an electron in a unit energy range about an energy e is twice the ideal gas density of states given by Eq. 11) For this distribution, Eq. 13) The upper limit in the integral is the chemical potential of the electron gas at 0 0 K, which is called the Fermi energy.
The fcc structure is distinct from the sc structure but is related to the latter by the symmetries of the unit cube. Both these lattice types belong to the cubic system. The primitive unit cell characterizing the fcc structure is shown in Fig. 2(b). The three edges of the unit cell are equal, but the cell is rhombohedral rather than cubic in shape. Both the conventional and primitive unit cells or Fig. 2 are valid representations of the fcc structure, but the primitive version is rarely used in practical applications.
Acoustical Impedance and the Theory of Horns and of the Phonograph (1919)(en)(8s) by Webster A. G.